Positive and monotone solutions of an m-point boundary value problem

Panos K. Palamides
Abstract:
We study the second-order ordinary differential equation
subject to the multi-point boundary conditions
We prove the existence of a positive solution (and monotone in some cases)
under superlinear and/or sublinear growth rate in
.
Our approach is based
on an analysis of the corresponding vector field on the
face-plane and on Kneser's property for the solution's funnel.